Question

利用矩阵的初等行变换，求逆矩阵

Answer 1

[A|E] =
1 1 1 1 1 0 0 0
-1 1 1 1 0 1 0 0
-1 -1 1 1 0 0 1 0
-1 -1 -1 1 0 0 0 1

=
1 1 1 1 1 0 0 0
0 2 2 2 1 1 0 0
0 0 2 2 1 0 1 0
0 0 0 2 1 0 0 1

=
1 1 1 1 1 0 0 0
0 2 2 2 1 1 0 0
0 0 2 2 1 0 1 0
0 0 0 1 1/2 0 0 1/2

[A|E] =
1 1 1 0 1/2 0 0 -1/2
0 2 2 0 0 1 0 -1
0 0 2 0 0 0 1 -1
0 0 0 1 1/2 0 0 1/2

[A|E] =
1 1 1 0 1/2 0 0 -1/2
0 2 2 0 0 1 0 -1
0 0 1 0 0 0 1/2 -1/2
0 0 0 1 1/2 0 0 1/2

[A|E] =
1 1 0 0 1/2 0 -1/2 0
0 2 0 0 0 1 -1 0
0 0 1 0 0 0 1/2 -1/2
0 0 0 1 1/2 0 0 1/2

[A|E] =
1 1 0 0 1/2 0 -1/2 0
0 1 0 0 0 1/2 -1/2 0
0 0 1 0 0 0 1/2 -1/2
0 0 0 1 1/2 0 0 1/2

[A|E] =
1 0 0 0 1/2 -1/2 0 0
0 1 0 0 0 1/2 -1/2 0
0 0 1 0 0 0 1/2 -1/2
0 0 0 1 1/2 0 0 1/2

A^(-1) =
1/2 -1/2 0 0
0 1/2 -1/2 0
0 0 1/2 -1/2
1/2 0 0 1/2

追问

第一步到第二步怎么来的

追答

将第1行
加到
第2,3,4行